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- // intersections.cpp
- //
- // Copyright (c) 2018
- // Justinas V. Daugmaudis
- //
- // Distributed under the Boost Software License, Version 1.0. (See
- // accompanying file LICENSE_1_0.txt or copy at
- // http://www.boost.org/LICENSE_1_0.txt)
- //[intersections
- /*`
- For the source of this example see
- [@boost://libs/random/example/intersections.cpp intersections.cpp].
- This example demonstrates generating quasi-randomly distributed chord
- entry and exit points on an S[sup 2] sphere.
- First we include the headers we need for __niederreiter_base2
- and __uniform_01 distribution.
- */
- #include <boost/random/niederreiter_base2.hpp>
- #include <boost/random/uniform_01.hpp>
- #include <boost/math/constants/constants.hpp>
- #include <boost/tuple/tuple.hpp>
- /*`
- We use 4-dimensional __niederreiter_base2 as a source of randomness.
- */
- boost::random::niederreiter_base2 gen(4);
- int main()
- {
- typedef boost::tuple<double, double, double> point_t;
- const std::size_t n_points = 100; // we will generate 100 points
- std::vector<point_t> points;
- points.reserve(n_points);
- /*<< __niederreiter_base2 produces integers in the range [0, 2[sup 64]-1].
- However, we want numbers in the range [0, 1). The distribution
- __uniform_01 performs this transformation.
- >>*/
- boost::random::uniform_01<double> dist;
- for (std::size_t i = 0; i != n_points; ++i)
- {
- /*`
- Using formula from J. Rovira et al., "Point sampling with uniformly distributed lines", 2005
- to compute uniformly distributed chord entry and exit points on the surface of a sphere.
- */
- double cos_theta = 1 - 2 * dist(gen);
- double sin_theta = std::sqrt(1 - cos_theta * cos_theta);
- double phi = boost::math::constants::two_pi<double>() * dist(gen);
- double sin_phi = std::sin(phi), cos_phi = std::cos(phi);
- point_t point_on_sphere(sin_theta*sin_phi, cos_theta, sin_theta*cos_phi);
- /*`
- Here we assume that our sphere is a unit sphere at origin. If your sphere was
- different then now would be the time to scale and translate the `point_on_sphere`.
- */
- points.push_back(point_on_sphere);
- }
- /*`
- Vector `points` now holds generated 3D points on a sphere.
- */
- return 0;
- }
- //]
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